Answered: tan x lim x o tan 2x

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 12E

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Question

Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result.

Expert Solution

Step 1

Given:

$\lim_{x \to 0} \frac{\tan x}{\tan 2 x}$

Step 2

Explanation:

Consider

$f (x) = \frac{\tan x}{\tan 2 x}$

Now create table as given below,

x	-0.05	-0.01	0.001	0.05
f(x)	0.4987	0.4999	0.4999	0.4987

As x tends to zero , f(x) tends to approximately 0.5

$\lim_{x \to 0} \frac{\tan x}{\tan 2 x} = 0.5$

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